Parametric joint-coding of audio sources

ABSTRACT

The following coding scenario is addressed: A number of audio source signals need to be transmitted or stored for the purpose of mixing wave field synthesis, multi-channel surround, or stereo signals after decoding the source signals. The proposed technique offers significant coding gain when jointly coding the source signals, compared to separately coding them, even when no redundancy is present between the source signals. This is possible by considering statistical properties of the source signals, the properties of mixing techniques, and spatial hearing. The sum of the source signals is transmitted plus the statistical properties of the source signals which mostly determine the perceptually important spatial cues of the final mixed audio channels. Source signals are recovered at the receiver such that their statistical properties approximate the corresponding properties of the original source signals. Subjective evaluations indicate that high audio quality is achieved by the proposed scheme.

BACKGROUND OF THE INVENTION I. Introduction

In a general coding problem, we have a number of (mono) source signalssi(n) (1≤i≤M) and a scene description vector S(n), where n is the timeindex. The scene description vector contains parameters such as(virtual) source positions, source widths, and acoustic parameters suchas (virtual) room parameters. The scene description may betime-invariant or may be changing over time. The source signals andscene description are coded and transmitted to a decoder. The codedsource signals, ŝi(n) are successively mixed as a function of the scenedescription, Ŝ(n), to generate wavefield synthesis, multi-channel, orstereo signals as a function of the scene description vector. Thedecoder output signals are denoted {circumflex over (x)}i(n) (0≤i≤N).Note that the scene description vector S(n) may not be transmitted butmay be determined at the decoder. In this document, the term “stereoaudio signal” always refers to two-channel stereo audio signals.

ISO/IEC MPEG-4 addresses the described coding scenario. It defines thescene description and uses for each (“natural”) source signal a separatemono audio coder, e.g. an AAC audio coder. However, when a complex scenewith many sources is to be mixed, the bitrate becomes high, i.e. thebitrate scales up with the number of sources. Coding one source signalwith high quality requires about 60-90 kb/s.

Previously, we addressed a special case of the described coding problem[1][2] with a scheme denoted Binaural Cue Coding (BCC) for FlexibleRendering. By transmitting only the sum of the given source signals pluslow bitrate side information, low bitrate is achieved. However, thesource signals can not be recovered at the decoder and the scheme waslimited to stereo and multi-channel surround signal generation. Also,only simplistic mixing was used, based on amplitude and delay panning.Thus, the direction of sources could be controlled but no other auditoryspatial image attributes. Another limitation of this scheme was itslimited audio quality. Especially, a decrease in audio quality as thenumber of source signals is increased.

The document [1], (Binaural Cue Coding, Parametric Stereo, MP3 Surround,MPEG Surround) covers the case where N audio channels are encoded and Naudio channels with similar cues then the original audio channels aredecoded. The transmitted side information includes inter-channel cueparameters relating to differences between the input channels.

The channels of stereo and multi-channel audio signals contain mixes ofaudio sources signals and are thus different in nature than pure audiosource signals. Stereo and multi-channel audio signals are mixed suchthat when played back over an appropriate playback system, the listenerwill perceive an auditory spatial image (“sound stage”) as captured bythe recording setup or designed by the recording engineer during mixing.A number of schemes for joint-coding for the channels of a stereo ormulti-channel audio signal have been proposed previously.

SUMMARY OF THE INVENTION

The aim of the invention is to provide a method to transmit a pluralityof source signals while using a minimum bandwidth. In most of knownmethods, the playback format (e.g. stereo, 5.1) is predefined and has adirect influence on the coding scenario. The audio stream on the decoderside should use only this predefined playback format, therefore bindingthe user to a predefined playback scenario (e.g. stereo).

The proposed invention encodes N audio source signals, typically notchannels of a stereo or multi-channel signals, but independent signals,such as different speech or instrument signals. The transmitted sideinformation includes statistical parameters relating to the input audiosource signals.

The proposed invention decodes M audio channels with different cues thanthe original audio source signals. These different cues are eitherimplicitly synthesized by applying a mixer to the received sum signal.The mixer is controlled as a function of the received statistical sourceinformation and the received (or locally determined) audio formatparameters and mixing parameters. Alternatively, these different cuesare explicitly computed as a function of the received statistical sourceinformation and the received (or locally determined) audio formatparameters and mixing parameters. These computed cues are used tocontrol a prior art decoder (Binaural Cue Coding, Parametric Stereo,MPEG Surround) for synthesizing the output channels given the receivedsum signal.

The proposed scheme for joint-coding of audio source signals is thefirst of its kind. It is designed for joint-coding of audio sourcesignals. Audio source signals are usually mono audio signals which arenot suitable for playback over a stereo or multi-channel audio system.For brevity, in the following, audio source signals are often denotedsource signals.

Audio source signals first need to be mixed to stereo, multi-channel, orwavefield synthesis audio signals prior to playback. An audio sourcesignal can be a single instrument or talker, or the sum of a number ofinstruments and talkers. Another type of audio source signal is a monoaudio signal captured with a spot microphone during a concert. Oftenaudio source signals are stored on multi-track recorders or in harddiskrecording systems.

The claimed scheme for joint-coding of audio source signals, is based ononly transmitting the sum of the audio source signals,

$\begin{matrix}{{{s(n)} = {\sum\limits_{i = 1}^{M}\; {s_{i}(n)}}},} & (1)\end{matrix}$

or a weighted sum of the source signals. Optionally, weighted summationcan be carried out with different weights in different subbands and theweights may be adapted in time.

Summation with equalization, as described in Chapter 3.3.2 in [1], mayalso be applied. In the following, when we refer to the sum or sumsignal, we always mean a signal generate by (1) or generated asdescribed. In addition to the sum signal, side information istransmitted. The sum and the side information represent the outputtedaudio stream. Optionally, the sum signal is coded using a conventionalmono audio coder. This stream can be stored in a file (CD, DVD,Harddisk) or broadcasted to the receiver. The side informationrepresents the statistical properties of the source signals which arethe most important factors determining the perceptual spatial cues ofthe mixer output signals. It will be shown that these properties aretemporally evolving spectral envelopes and auto-correlation functions.About 3 kb/s of side information is transmitted per source signal. Atthe receiver, source signals ŝi(n) (1≤i≤M) are recovered with the beforementioned statistical properties approximating the correspondingproperties of the original source signals and the sum signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood thanks to the attached Figuresin which:

FIG. 1 shows a scheme in which the transmission of each source signal ismade independently for further processing.

FIG. 2 shows a number of sources transmitted as sum signal plus sideinformation.

FIG. 3 shows a block diagram of a Binaural Cue Coding (BCC) scheme.

FIG. 4 shows a mixer for generating stereo signals based on severalsource signals.

FIG. 5 shows the dependence between ICTD, ICLD and ICC and the sourcesignal subband power.

FIG. 6 shows the process of side information generation.

FIG. 7 shows the process of estimating the LPC parameters of each sourcesignal.

FIG. 8 shows the process of re-creating the source signals from a sumsignal.

FIG. 9 shows an alternative scheme for the generation of each signalfrom the sum signal.

FIG. 10 shows a mixer for generating stereo signals based on the sumsignal.

FIG. 11 shows an amplitude panning algorithm preventing that the sourcelevels depends on the mixing parameters.

FIG. 12 shows a loudspeaker array of a wavefield synthesis playbacksystem.

FIG. 13 shows how to recover an estimate of the source signals at thereceiver by processing the downmix of the transmitted channels.

FIG. 14 shows how to recover an estimate of the source signals at thereceiver by processing the transmitted channels.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS II. Definitions,Notations, and Variables

The following notation and variables are used in this paper:

n time index;i audio channel or source index;d delay index;M number of encoder input source signals;N number of decoder output channels;x_(i)(n) mixed original source signals;{circumflex over (x)}_(i)(n) mixed decoder output signals;s_(i)(n) encoder input source signals;ŝ_(i)(n) transmitted source signals also called pseudo-source signals;s(n) transmitted sum signal;y_(i)(n) L-channel audio signal; (audio signal to be re-mixed);{tilde over (s)}_(i)(k) one subband signal of s_(i)(n) (similarlydefined for other signals);Ε{{tilde over (s)}_(i) ²(n)} short-time estimate of {tilde over (s)}_(i)²(n) (similarly defined for other signals);ICLD inter-channel level difference;ICTD inter-channel time difference;ICC inter-channel coherence;ΔL(n) estimated subband ICLD;τ(n) estimated subband ICTD;c(n) estimated subband ICC;{tilde over (p)}_(i)(n) relative source subband power;a_(i), b_(i) mixer scale factors;c_(i), d_(i) mixer delays;ΔL_(i), τ(n) mixer level and time difference;G_(i) mixer source gain;

III. Joint-Coding of Audio Source Signals

First, Binaural Cue Coding (BCC), a parametric multi-channel audiocoding technique, is described. Then it is shown that with the sameinsight as BCC is based on one can devise an algorithm for jointlycoding the source signals for a coding scenario.

A. Binaural Cue Coding (BCC)

A BCC scheme [1][2] for multi-channel audio coding is shown in thefigure bellow. The input multi-channel audio signal is downmixed to asingle channel. As opposed to coding and transmitting information aboutall channel waveforms, only the downmixed signal is coded (with aconventional mono audio coder) and transmitted. Additionally,perceptually motivated “audio channel differences” are estimated betweenthe original audio channels and also transmitted to the decoder. Thedecoder generates its output channels such that the audio channeldifferences approximate the corresponding audio channel differences ofthe original audio signal.

Summing localization implies that perceptually relevant audio channeldifferences for a loudspeaker signal channel pair are the inter-channeltime difference (ICTD) and inter-channel level difference (ICLD). ICTDand ICLD can be related to the perceived direction of auditory events.Other auditory spatial image attributes, such as apparent source widthand listener envelopment, can be related to interaural coherence (IC).For loudspeaker pairs in the front or back of a listener, the interauralcoherence is often directly related to the inter-channel coherence (ICC)which is thus considered as third audio channel difference measure byBCC. ICTD, ICLD, and ICC are estimated in subbands as a function oftime. Both, the spectral and temporal resolution that is used, aremotivated by perception.

B. Parametric Joint-Coding of Audio Sources

A BCC decoder is able to generate a multi-channel audio signal with anyauditory spatial image by taking a mono signal and synthesizing atregular time intervals a single specific ICTD, ICLD, and ICC cue persubband and channel pair. The good performance of BCC schemes for a widerange of audio material [see 1] implies that the perceived auditoryspatial image is largely determined by the ICTD, ICLD, and ICC.Therefore, as opposed to requiring “clean” source signals s_(i)(n) asmixer input in FIG. 1, we just require pseudo-source signals ŝ_(i)(n)with the property that they result in similar ICTD, ICLD, and ICC at themixer output as for the case of supplying the real source signals to themixer. There are three goals for the generation of ŝ_(i)(n):

-   -   If ŝ_(i)(n) are supplied to a mixer, the mixer output channels        will have approximately the same spatial cues (ICLD, ICTD, ICC)        as if s_(i)(n) were supplied to the mixer.    -   ŝ_(i)(n) are to be generated with as little as possible        information about the original source signals s(n) (because the        goal is to have low bitrate side information).    -   ŝ_(i)(n) are generated from the transmitted sum signal s(n) such        that a minimum amount of signal distortion is introduced.

For deriving the proposed scheme we are considering a stereo mixer(M=2). A further simplification over the general case is that onlyamplitude and delay panning are applied for mixing. If the discretesource signals were available at the decoder, a stereo signal would bemixed as shown in FIG. 4, i.e.

$\begin{matrix}{{x_{1}(n)} = {{\sum\limits_{i = 1}^{M}\; {a_{i}{s_{i}( {n - c_{i}} )}\mspace{14mu} {x_{2}(n)}}} = {\sum\limits_{i = 1}^{M}\; {b_{i}{s_{i}( {n - d_{i}} )}}}}} & (2)\end{matrix}$

In this case, the scene description vector S(n) contains just sourcedirections which determine the mixing parameters,

M(n)=(a ₁ ,a ₂ , . . . ,a _(M) ,b ₁ ,b ₂ , . . . ,b _(M) ,c ₁ ,c ₂ , . .. ,c _(M) ,d ₁ ,d ₂ , . . . ,d _(M))^(T)  □

where T is the transpose of a vector. Note that for the mixingparameters we ignored the time index for convenience of notation.

More convenient parameters for controlling the mixer are time and leveldifference, T_(i) and ΔL_(i), which are related to a_(i), b_(i), c_(i),and d_(i) by

$\begin{matrix}{{a_{i} = \frac{10^{{Gi}\text{/}20}}{\sqrt{1 + 10^{\Delta \; {Li}\text{/}10}}}}\mspace{14mu} {b_{i} = {10^{{({{Gi} + {\Delta \; {Li}}})}\text{/}20}a_{i}}}\mspace{14mu} {c_{i} = {\max \mspace{14mu} \{ {{- T_{i}},0} \}}}\mspace{14mu} {d_{i} = {\max \mspace{14mu} \{ {T_{i},0} \}}}} & (4)\end{matrix}$

where G_(i) is a source gain factor in dB.

In the following, we are computing ICTD, ICLD, and ICC of the stereomixer output as a function of the input source signals s_(i)(n). Theobtained expressions will give indication which source signal propertiesdetermine ICTD, ICLD, and ICC (together with the mixing parameters).ŝ_(i) (n) are then generated such that the identified source signalproperties approximate the corresponding properties of the originalsource signals.

B.1 ICTD, ICLD, and ICC of the Mixer Output

The cues are estimated in subbands and as a function of time. In thefollowing it is assumed that the source signals s_(i)(n) are zero meanand mutually independent. A pair of subband signals of the mixer output(2) is denoted {circumflex over (x)}₁(n) and {circumflex over (x)}₂(n).Note that for simplicity of notation we are using the same time index nfor time-domain and subband-domain signals. Also, no subband index isused and the described analysis/processing is applied to each subbandindependently. The subband power of the two mixer output signals is

$\begin{matrix} {{ {{E\{ {{\overset{\sim}{x}}_{1}^{2}(n)} \}} = {\sum\limits_{i = 1}^{M}\; {a_{i}^{2}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} )}}} \} \mspace{14mu} E\{ {{\overset{\sim}{x}}_{2}^{2}(n)} \}} = {\sum\limits_{i = 1}^{M}\; {b_{i}^{2}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} )}}} \} & (5)\end{matrix}$

where {tilde over (s)}_(i)(n) is one subband signal of source s_(i)(n)and E{.} denotes short-time expectation, e.g.

$\begin{matrix}{{E\{ {{\overset{\sim}{s}}_{2}^{2}(n)} \}} = {\frac{1}{K}{\sum\limits_{n - {K\text{/}2}}^{n + {K\text{/}2} - 1}{{\overset{\sim}{s}}_{i}^{2}(n)}}}} & (6)\end{matrix}$

where K determines the length of the moving average. Note that thesubband power values E{{tilde over (s)}₂ ²(n)} represent for each sourcesignal the spectral envelope as a function of time. The ICLD, ΔL(n), is

$\begin{matrix}{{\Delta \; {L(n)}} = {10\mspace{14mu} \log_{10}\frac{ {\sum_{i = 1}^{M}{b_{1}^{2}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} )}} \}}{ {\sum_{i = 1}^{M}{a_{i}^{2}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} )}} \}}}} & (7)\end{matrix}$

For estimating ICTD and ICC the normalized cross-correlation function,

$\begin{matrix}{{\Phi ( {n,d} )} = \frac{E\{ {{{\overset{\sim}{x}}_{1}(n)}{{\overset{\sim}{x}}_{2}( {n + d} )}} \}}{\sqrt{E\{ {{\overset{\sim}{x}}_{1}^{2}(n)} \} E\{ {{\overset{\sim}{x}}_{2}^{2}( {n + d} )} \}}}} & (8)\end{matrix}$

is estimated. The ICC, c(n), is computed according to

$\begin{matrix}{{c(n)} = {\max\limits_{d}{\Phi ( {n,d} )}}} & (9)\end{matrix}$

For the computation of the ICTD, T(n), the location of the highest peakon the delay axis is computed,

$\begin{matrix}{{T(n)} = {\arg \mspace{14mu} {\max\limits_{d}{\Phi ( {n,d} )}}}} & (10)\end{matrix}$

Now the question is, how can the normalized cross-correlation functionbe computed as a function of the mixing parameters. Together with (2),(8) can be written as

$\begin{matrix}{{\Phi ( {n,d} )} = \frac{\sum_{i = 1}^{M}{E\{ {a_{i}b_{i}{{\overset{\sim}{s}}_{i}( {n - c_{i}} )}{{\overset{\sim}{s}}_{i}( {n - d_{i} + d} )}} \}}}{\sqrt{E\{ {\sum_{i = 1}^{M}{a_{i}^{2}{s_{i}^{2}( {n - c_{i}} )}}} \} E\{ {\sum_{i = 1}^{M}{b_{i}^{2}{s_{i}^{2}( {n - d_{i}} )}}} \}}}} & (11)\end{matrix}$

which is equivalent to

$\begin{matrix}{{\Phi ( {n,d} )} = \frac{\sum_{i = 1}^{M}{a_{i}b_{i}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} \} {\Phi_{i}( {n,{d_{i} - T_{i}}} )}}}{\sqrt{( {\sum_{i = 1}^{M}{a_{i}^{2}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} \}}} )\{ {\sum_{i = 1}^{M}{b_{i}^{2}E\{ {s_{i}^{2}(n)} \}}} )}}} & (12)\end{matrix}$

where the normalized auto-correlation function Φ(n,e) is

$\begin{matrix}{{\Phi ( {n,e} )} = \frac{E\{ {{s_{i}(n)}{s_{i}( {n + e} )}} \}}{E\{ {s_{i}^{2}(n)} \}}} & (13)\end{matrix}$

and T_(i)=d_(i)−c_(i). Note that for computing (12) given (11) it hasbeen assumed that the signals are wide sense stationary within theconsidered range of delays, i.e.

Ε{{tilde over (s)}_(i) ²(n)}=E{{tilde over (s)} _(i) ²(n−c _(i))}

E{{tilde over (s)} _(i) ²(n)}=E{{tilde over (s)} _(i) ²(n−d _(i))}

Ε{{tilde over (s)}_(i)(n){tilde over (s)}_(i)(n+c _(i) −d _(i)+d)}}=Ε{{tilde over (s)}_(i)(n−c _(i)){tilde over (s)}_(i)(n−d _(i) +d)}

A numerical example for two source signals, illustrating the dependencebetween ICTD, ICLD, and ICC and the source subband power, is shown inFIG. 5. The top, middle, and bottom panel of FIG. 5 show ΔL(n), T(n),and c(n), respectively, as a function of the ratio of the subband powerof the two source signals, a=Ε{{tilde over (s)}₁ ²(n)}/Ε{{tilde over(s)}₁ ²(n)}+Ε{{tilde over (s)}₂ ²(n)}), for different mixing parameters(4) ΔL₁, ΔL₂, T₁ and T₂. Note that when only one source has power in thesubband (a=0 or a=1), then the computed ΔL(n) and T(n) are equal to themixing parameters (ΔL₁, ΔL₂, T₁, T₂).

B.2 Necessary Side Information

The ICLD (7) depends on the mixing parameters (a_(i), b_(i), c_(i),d_(i)) and on the short-time subband power of the sources, Ε{{tilde over(s)}_(i) ²(n)} (6). The normalized subband cross-correlation functionΦ(n,d) (12), that is needed for ICTD (10) and ICC (9) computation,depends on Ε{{tilde over (s)}_(i) ²(n)} and additionally on thenormalized subband auto-correlation function, Φ_(i)(n, e) (13), for eachsource signal. The maximum of Φ(n,d) lies within the rangemin_(i){T_(i)}≤d≤max_(i){T_(i)}. For source i with mixer parameterT_(i)=d_(i)−c_(i), the corresponding range for which the source signalsubband property Φ_(i)(n, e) (13) is needed is

$\begin{matrix}{{{\min\limits_{l}\{ T_{l} \}} - T_{i}} \leq e \leq {{\max\limits_{l}\{ T_{l} \}} - T_{i}}} & (14)\end{matrix}$

Since the ICTD, ICLD, and ICC cues depend on the source signal subbandproperties Ε{{tilde over (s)}_(i) ²(n)} and Φ_(i)(n, e) in the range(14), in principle these source signal subband properties need to betransmitted as side information. We assume that any other kind of mixer(e.g. mixer with effects, wavefield synthesis mixer/convoluter, etc.)has similar properties and thus this side information is useful alsowhen other mixers than the described one are used. For reducing theamount of side information, one could store a set of predefinedauto-correlation functions in the decoder and only transmit indices forchoosing the ones most closely matching the source signal properties. Afirst version of our algorithm assumes that within the range (14)Φ_(i)(n, e)=1 and thus (12) is computed using only the subband powervalues (6) as side information. The data shown in FIG. 5 has beencomputed assuming Φ_(i)(n, e)=1.

In order to reduce the amount of side information, the relative dynamicrange of the source signals is limited. At each time, for each subbandthe power of the strongest source is selected. We found it sufficient tolower bound the corresponding subband power of all the other sources ata value 24 dB lower than the strongest subband power. Thus the dynamicrange of the quantizer can be limited to 24 dB.

Assuming that the source signals are independent, the decoder cancompute the sum of the subband power of all sources as Ε{{tilde over(s)}²(n)}. Thus, in principle it is enough to transmit to the decoderonly the subband power values of M−1 sources, while the subband power ofthe remaining source can be computed locally. Given this idea, the sideinformation rate can be slightly reduced by transmitting the subbandpower of sources with indices 2≤i≤M relative to the power of the firstsource,

$\begin{matrix}{{\Delta \; {{\overset{\sim}{p}}_{i}(n)}} = {10\mspace{14mu} \log_{10}{\frac{E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} \}}{E\{ {{\overset{\sim}{s}}_{1}^{2}(n)} \}}.}}} & (15)\end{matrix}$

Note that dynamic range limiting as described previously is carried outprior to (15). As an alternative, the subband power values could benormalized relative to the sum signal subband power, as opposed tonormalization relative to one source's subband power (15). For asampling frequency of 44.1 kHz we use 20 subbands and transmit for eachsubband Δ{tilde over (p)}_(i)(n) (2≤i≤M) about every 12 ms. 20 subbandscorresponds to half the spectral resolution of the auditory system (onesubband is two “critical bandwidths” wide). Informal experimentsindicate that only slight improvement is achieved by using more subbandsthan 20, e.g. 40 subbands. The number of subbands and subband bandwidthsare chosen according to the time and frequency resolution of theauditory system. A low quality implementation of the scheme requires atleast three subbands (low, medium, high frequencies).

According to a particular embodiment, the subbands have differentbandwidths, subbands at lower frequencies have smaller bandwidth thansubbands at higher frequencies.

The relative power values are quantized with a scheme similar to theICLD quantizer described in [2], resulting in a bitrate of approximately3(M−1) kb/s. FIG. 6 illustrates the process of side informationgeneration (corresponds to the “Side information generation” block inFIG. 2).

Side information rate can be additionally reduced by analyzing theactivity for each source signal and only transmitting the sideinformation associated with the source if it is active.

As opposed to transmitting the subband power values Ε{{tilde over(s)}_(i) ²(n)} as statistical information, other informationrepresenting the spectral envelopes of the source signals could betransmitted. For example, linear predictive coding (LPC) parameterscould be transmitted, or corresponding other parameters such as latticefilter parameters or line spectral pair (LSP) parameters. The process ofestimating the LPC parameters of each source signal is illustrated inFIG. 7.

B.3 Computing ŝ_(i)(n)

FIG. 8 illustrates the process that is used to re-create the sourcesignals, given the sum signal (1). This process is part of the“Synthesis” block in FIG. 2. The individual source signals are recoveredby scaling each subband of the sum signal with g_(i)(n) and by applyinga de-correlation filter with impulse response h_(i)(n),

$\begin{matrix}{{{\hat{\overset{\sim}{s}}}_{i}(n)} = {{{h_{i}(n)}*( {{g_{i}(n)}\mspace{14mu} \overset{\sim}{s}\mspace{14mu} (n)} )} = {{h_{i}(n)}*( \sqrt{\frac{E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} \}}{E\{ {{\overset{\sim}{s}}^{2}(n)} \}}{\overset{\sim}{s}(n)}} )}}} & (16)\end{matrix}$

where * is the linear convolution operator and Ε{{tilde over (s)}_(i)²(n)} is computed with the side information by

$\begin{matrix}{{E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} \}} = {{1\text{/}\sqrt{1 + {\sum_{i = 2}^{M}10^{\frac{\Delta \; {{\overset{\sim}{p}}_{i}{(n)}}}{10}}}}\mspace{14mu} {for}\mspace{14mu} i} = {1\mspace{14mu} {or}\mspace{14mu} 10^{\frac{\Delta \; {{\overset{\sim}{p}}_{i}{(n)}}}{10}}E\{ {{\overset{\sim}{s}}_{1}^{2}(n)} \} \mspace{14mu} {otherwise}}}} & (17)\end{matrix}$

As de-correlation filters h_(i)(n), complementary comb filters, all-passfilters, delays, or filters with random impulse responses may be used.The goal for the de-correlation process is to reduce correlation betweenthe signals while not modifying how the individual waveforms areperceived. Different de-correlation techniques cause differentartifacts. Complementary comb filters cause coloration. All thedescribed techniques are spreading the energy of transients in timecausing artifacts such as “pre-echoes”. Given their potential forartifacts, de-correlation techniques should be applied as little aspossible. The next section describes techniques and strategies whichrequire less de-correlation processing than simple generation ofindependent signals ŝ_(i)(n).

An alternative scheme for generation of the signals ŝ_(i)(n) is shown inFIG. 9. First the spectrum of s(n) is flattened by means of computingthe linear prediction error e(n). Then, given the LPC filters estimatedat the encoder, f_(i), the corresponding all-pole filters are computedas the inverse z-transform of

${{\overset{\_}{F}}_{i}(z)} = \frac{1}{1 - {z^{- 1}{F_{i}(z)}}}$

The resulting all-pole filters, ƒ _(i), represent the spectral envelopeof the source signals. If other side information than LPC parameters istransmitted, the LPC parameters first need to be computed as a functionof the side information. As in the other scheme, de-correlation filtersh_(i) are used for making the source signals independent.

IV. Implementations Considering Practical Constraints

In the first part of this section, an implementation example is given,using a BCC synthesis scheme as a stereo or multi-channel mixer. This isparticularly interesting since such a BCC type synthesis scheme is partof an upcoming ISO/IEC MPEG standard, denoted “spatial audio coding” .The source signals ŝ_(i)(n) are not explicitly computed in this case,resulting in reduced computational complexity. Also, this scheme offersthe potential for better audio quality since effectively lessde-correlation is needed than for the case when the source signalsŝ_(i)(n) are explicitly computed.

The second part of this section discusses issues when the proposedscheme is applied with any mixer and no de-correlation processing isapplied at all. Such a scheme has a lower complexity than a scheme withde-correlation processing, but may have other drawbacks as will bediscussed.

Ideally, one would like to apply de-correlation processing such that thegenerated ŝ_(i)(n) can be considered independent. However, sincede-correlation processing is problematic in terms of introducingartifacts, one would like to apply de-correlation processing as littleas possible. The third part of this section discusses how the amount ofproblematic de-correlation processing can be reduced while gettingbenefits as if the generated ŝ_(i)(n) were independent.

A. Implementation Without Explicit Computation of ŝ_(i)(n)

Mixing is directly applied to the transmitted sum signal (1) withoutexplicit computation of ŝ_(i)(n). A BCC synthesis scheme is used forthis purpose. In the following, we are considering the stereo case, butall the described principles can be applied for generation ofmulti-channel audio signals as well.

A stereo BCC synthesis scheme (or a “parametric stereo” scheme), appliedfor processing the sum signal (1), is shown in FIG. 10. Desired would bethat the BCC synthesis scheme generates a signal that is perceivedsimilarly as the output signal of a mixer as shown in FIG. 4. This isso, when ICTD, ICLD, and ICC between the BCC synthesis scheme outputchannels are similar as the corresponding cues appearing between themixer output (4) signal channels.

The same side information as for the previously described more generalscheme is used, allowing the decoder to compute the short-time subbandpower values Ε{{tilde over (s)}_(i) ²(n)} of the sources. Given Ε{{tildeover (s)}_(i) ²(n)}, the gain factors g₁ and g₂ in FIG. 10 are computedas

$\begin{matrix}{{g_{1}(n)} = {{\sqrt{\frac{\sum_{i = 1}^{M}{a_{i}^{2}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} \}}}{E\{ {{\overset{\sim}{s}}^{2}(n)} \}}}\mspace{14mu} {g_{2}(n)}} = \sqrt{\frac{\sum_{i = 1}^{M}{b_{i}^{2}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} \}}}{E\{ {{\overset{\sim}{s}}^{2}(n)} \}}}}} & (18)\end{matrix}$

such that the output subband power and ICLD (7) are the same as for themixer in FIG. 4. The ICTD T(n) is computed according to (10),determining the delays D₁ and D₂ in FIG. 10,

D ₁(n)=max{−T(n), o} D ₂(n)=max{T(n), 0}  (19)

The ICC c(n) is computed according to (9) determining the de-correlationprocessing in FIG. 10. De-correlation processing (ICC synthesis) isdescribed in [1]. The advantages of applying de-correlation processingto the mixer output channels compared to applying it for generatingindependent ŝ_(i)(n) are:

-   -   Usually the number of source signals M is larger than the number        of audio output channels N. Thus, the number of independent        audio channels that need to be generated is smaller when        de-correlating the N output channels as opposed to        de-correlating the M source signals.    -   Often the N audio output channels are correlated (ICC>0) and        less de-correlation processing can be applied than would be        needed for generating independent M or N channels.        Due to less de-correlation processing better audio quality is        expected.

Best audio quality is expected when the mixer parameters are constrainedsuch that a_(i) ²+b_(i) ²=1, i.e. G_(i)=0 dB. In this case, the power ofeach source in the transmitted sum signal (1) is the same as the powerof the same source in the mixed decoder output signal. The decoderoutput signal (FIG. 10) is the same as if the mixer output signal (FIG.4) were encoded and decoded by a BCC encoder/decoder in this case. Thus,also similar quality can be expected.

The decoder can not only determine the direction at which each source isto appear but also the gain of each source can be varied. The gain isincreased by choosing a_(i) ²+b_(i) ²>1 (G_(i)>dB) and decreased bychoosing a_(i) ²+b_(i) ²<1 (G_(i)<0 dB).

B. Using No De-Correlation Processing

The restriction of the previously described technique is that mixing iscarried out with a BCC synthesis scheme. One could imagine implementingnot only ICTD, ICLD, and ICC synthesis but additionally effectsprocessing within the BCC synthesis.

However, it may be desired that existing mixers and effects processorscan be used. This also includes wavefield synthesis mixers (oftendenoted “convoluters”). For using existing mixers and effectsprocessors, the ŝ_(i)(n) are computed explicitly and used as if theywere the original source signals.

When applying no de-correlation processing (h_(i)(n)=δ(n) in (16)) goodaudio quality can also be achieved. It is a compromise between artifactsintroduced due to de-correlation processing and artifacts due to thefact that the source signals ŝ_(i)(n) are correlated. When node-correlation processing is used the resulting auditory spatial imagemay suffer from instability [1]. But the mixer may introduce itself somede-correlation when reverberators or other effects are used and thusthere is less need for de-correlation processing.

If ŝ_(i)(n) are generated without de-correlation processing, the levelof the sources depends on the direction to which they are mixed relativeto the other sources. By replacing amplitude panning algorithms inexisting mixers with an algorithm compensating for this leveldependence, the negative effect of loudness dependence on mixingparameters can be circumvented. A level compensating amplitude algorithmis shown in FIG. 11 which aims to compensate the source level dependenceon mixing parameters. Given the gain factors of a conventional amplitudepanning algorithm (e.g. FIG. 4), a_(i) and b_(i), the weights in FIG.11, ā_(i) and b _(i), are computed by

$\begin{matrix}{{{\overset{\_}{a}}_{i}(n)} = {{\sqrt{\frac{\sum_{i = 1}^{M}{a_{i}^{2}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} \}}}{E\{ ( {\sum_{i = 1}^{M}{a_{i}{{\overset{\sim}{s}}_{i}(n)}}} )^{2} \}}}\mspace{14mu} {and}\mspace{14mu} {{\overset{\_}{b}}_{i}(n)}} = \sqrt{\frac{\sum_{i = 1}^{M}{b_{i}^{2}E\{ {{\overset{\sim}{s}}_{i}^{2}(n)} \}}}{E\{ ( {\sum_{i = 1}^{M}{b_{i}{{\overset{\sim}{s}}_{i}(n)}}} )^{2} \}}}}} & (20)\end{matrix}$

Note that ā_(i) and b _(i) are computed such that the output subbandpower is the same as if ŝ_(i)(n) were independent in each subband.

c. Reducing the Amount of De-Correlation Processing

As mentioned previously, the generation of independent ŝ_(i)(n) isproblematic. Here strategies are described for applying lessde-correlation processing, while effectively getting a similar effect asif the ŝ_(i)(n) were independent.

Consider for example a wavefield synthesis system as shown in FIG. 12.The desired virtual source positions for s₁, s₂, . . . , s₆ (M=6) areindicated. A strategy for computing ŝ_(i)(n) (16) without generating Mfully independent signals is:

-   -   1. Generate groups of source indices corresponding to sources        close to each other. For example in FIG. 8 these could be: {1},        {2, 5}, {3}, and {4, 6}.    -   2. At each time in each subband select the source index of the        strongest source,

$\begin{matrix}{i_{\max} = {\max\limits_{i}{E\{ {\overset{\_}{s}(n)} \}}}} & (21)\end{matrix}$

Apply no de-correlation processing for the source indices part of thegroup containing i_(max), i.e. h_(i)(n)=δ(n).

-   -   3. For each other group choose the same h_(i)(n) within the        group.

The described algorithm modifies the strongest signal components least.Additionally, the number of different h_(i)(n) that are used arereduced. This is an advantage because de-correlation is easier the lessindependent channels need to be generated. The described technique isalso applicable when stereo or multi-channel audio signals are mixed.

V. Scalability in Terms of Quality and Bitrate

The proposed scheme transmits only the sum of all source signals, whichcan be coded with a conventional mono audio coder. When no monobackwards compatibility is needed and capacity is available fortransmission/storage of more than one audio waveform, the proposedscheme can be scaled for use with more than one transmission channel.This is implemented by generating several sum signals with differentsubsets of the given source signals, i.e. to each subset of sourcesignals the proposed coding scheme is applied individually. Audioquality is expected to improve as the number of transmitted audiochannels is increased because less independent channels have to begenerated by de-correlation from each transmitted channel (compared tothe case of one transmitted channel).

VI. Backwards Compatibility to Existing Stereo and Surround AudioFormats

Consider the following audio delivery scenario. A consumer obtains amaximum quality stereo or multi-channel surround signal (e.g. by meansof an audio CD, DVD, or on-line music store, etc.). The goal is tooptionally deliver to the consumer the flexibility to generate a custommix of the obtained audio content, without compromising standardstereo/surround playback quality.

This is implemented by delivering to the consumer (e.g. as optionalbuying option in an on-line music store) a bit stream of sideinformation which allows computation of ŝ_(i)(n) as a function of thegiven stereo or multi-channel audio signal. The consumer's mixingalgorithm is then applied to the ŝ_(i)(n). In the following, twopossibilities for computing ŝ_(i)(n), given stereo or multi-channelaudio signals, are described.

A. Estimating the Sum of the Source Signals at the Receiver

The most straight forward way of using the proposed coding scheme with astereo or multi-channel audio transmission is illustrated in FIG. 13,where y_(i)(n) (1≤i≤L) are the L channels of the given stereo ormulti-channel audio signal. The sum signal of the sources is estimatedby downmixing the transmitted channels to a single audio channel.Downmixing is carried out by means of computing the sum of the channelsy_(i)(n) (1≤i≤L) or more sophisticated techniques may be applied.

For best performance, it is recommended that the level of the sourcesignals is adapted prior to Ε{{tilde over (s)}_(i) ²(n)} estimation (6)such that the power ratio between the source signals approximates thepower ratio with which the sources are contained in the given stereo ormulti-channel signal. In this case, the downmix of the transmittedchannels is a relatively good estimate of the sum of the sources (1) (ora scaled version thereof).

An automated process may be used to adjust the level of the encodersource signal inputs s_(i)(n) prior to computation of the sideinformation. This process adaptively in time estimates the level atwhich each source signal is contained in the given stereo ormulti-channel signal. Prior to side information computation, the levelof each source signal is then adaptively in time adjusted such that itis equal to the level at which the source is contained in the stereo ormulti-channel audio signal.

B. Using the Transmitted Channels Individually

FIG. 14 shows a different implementation of the proposed scheme withstereo or multi-channel surround signal transmission. Here, thetransmitted channels are not downmixed, but used individually forgeneration of the ŝ_(i)(n). Most generally, the subband signals ofŝ_(i)(n) are computed by

$\begin{matrix}{{{\hat{\overset{\sim}{s}}}_{i}(n)} = {{h_{i}(n)}*( {{g_{i}(n)}{\sum\limits_{l = 1}^{L}\; {{w_{l}(n)}{{\overset{\sim}{y}}_{l}(n)}}}} )}} & (22)\end{matrix}$

where w_(l)(n) are weights determining specific linear combinations ofthe transmitted channels' subbands. The linear combinations are chosensuch that the ŝ_(i)(n) are already as much decorrelated as possible.Thus, no or only a small amount of de-correlation processing needs to beapplied, which is favorable as discussed earlier.

VII. Applications

Already previously we mentioned a number of applications for theproposed coding schemes. Here, we summarize these and mention a few moreapplications.

A. Audio Coding for Mixing

Whenever audio source signals need to be stored or transmitted prior tomixing them to stereo, multi-channel, or wavefield synthesis audiosignals, the proposed scheme can be applied. With prior art, a monoaudio coder would be applied to each source signal independently,resulting in a bitrate which scales with the number of sources. Theproposed coding scheme can encode a high number of audio source signalswith a single mono audio coder plus relatively low bitrate sideinformation. As described in Section V, the audio quality can beimproved by using more than one transmitted channel, if thememory/capacity to do so is available.

B. Re-Mixing With Meta-Data

As described in Section VI, existing stereo and multi-channel audiosignals can be re-mixed with the help of additional side information(i.e. “meta-data”). As opposed to only selling optimized stereo andmulti-channel mixed audio content, meta data can be sold allowing a userto re-mix his stereo and multi-channel music. This can for example alsobe used for attenuating the vocals in a song for karaoke, or forattenuating specific instruments for playing an instrument along themusic.

Even if storage would not be an issue, the described scheme would bevery attractive for enabling custom mixing of music. That is, because itis likely that the music industry would never be willing to give awaythe multi-track recordings. There is too much a danger for abuse. Theproposed scheme enables re-mixing capability without giving away themulti-track recordings.

Furthermore, as soon as stereo or multi-channel signals are re-mixed acertain degree of quality reduction occurs, making illegal distributionof re-mixes less attractive.

c. Stereo/Multi-Channel to Wavefield Synthesis Conversion

Another application for the scheme described in Section VI is describedin the following. The stereo and multi-channel (e.g. 5.1 surround) audioaccompanying moving pictures can be extended for wavefield synthesisrendering by adding side information. For example, Dolby AC-3 (audio onDVD) can be extended for 5.1 backwards compatibly coding audio forwavefield synthesis systems, i.e. DVDs play back 5.1 surround sound onconventional legacy players and wavefield synthesis sound on a newgeneration of players supporting processing of the side information.

VIII. Subjective Evaluations

We implemented a real-time decoder of the algorithms proposed in SectionIV-A and IV-B. An FFT-based STFT filterbank is used. A 1024-point FFTand a STFT window size of 768 (with zero padding) are used. The spectralcoefficients are grouped together such that each group represents signalwith a bandwidth of two times the equivalent rectangular bandwidth(ERB). Informal listening revealed that the audio quality did notnotably improve when choosing higher frequency resolution. A lowerfrequency resolution is favorable since it results in less parameters tobe transmitted.

For each source, the amplitude/delay panning and gain can be adjustedindividually. The algorithm was used for coding of several multi-trackaudio recordings with 12-14 tracks.

The decoder allows 5.1 surround mixing using a vector base amplitudepanning (VBAP) mixer. Direction and gain of each source signal can beadjusted. The software allows on the-fly switching between mixing thecoded source signal and mixing the original discrete source signals.

Casual listening usually reveals no or little difference between mixingthe coded or original source signals if for each source a gain G_(i) ofzero dB is used. The more the source gains are varied the more artifactsoccur. Slight amplification and attenuation of the sources (e.g. up to±6 dB) still sounds good. A critical scenario is when all the sourcesare mixed to one side and only a single source to the other oppositeside. In this case the audio quality may be reduced, depending on thespecific mixing and source signals.

IX. Conclusions

A coding scheme for joint-coding of audio source signals, e.g. thechannels of a multi-track recording, was proposed. The goal is not tocode the source signal waveforms with high quality, in which casejoint-coding would give minimal coding gain since the audio sources areusually independent. The goal is that when the coded source signals aremixed a high quality audio signal is obtained. By consideringstatistical properties of the source signals, the properties of mixingschemes, and spatial hearing it was shown that significant coding gainimprovement is achieved by jointly coding the source signals.

The coding gain improvement is due to the fact that only one audiowaveform is transmitted.

Additionally side information, representing the statistical propertiesof the source signals which are the relevant factors determining thespatial perception of the final mixed signal, are transmitted.

The side information rate is about 3 kbs per source signal. Any mixercan be applied with the coded source signals, e.g. stereo,multi-channel, or wavefield synthesis mixers.

It is straight forward to scale the proposed scheme for higher bitrateand quality by means of transmitting more than one audio channel.Furthermore, a variation of the scheme was proposed which allowsre-mixing of the given stereo or multi-channel audio signal (and evenchanging of the audio format, e.g. stereo to multi-channel or wavefieldsynthesis).

The applications of the proposed scheme are manifold. For example MPEG-4could be extended with the proposed scheme to reduce bitrate when morethan one “natural audio object” (source signal) needs to be transmitted.Also, the proposed scheme offers compact representation of content forwavefield synthesis systems. As mentioned, existing stereo ormulti-channel signals could be complemented with side information toallow that the user re-mixes the signals to his liking.

REFERENCES

[1] C. Faller, Parametric Coding of Spatial Audio, Ph.D. thesis, SwissFederal Institute of Technology Lausanne (EPFL), 2004, Ph.D. Thesis No.3062.[2] C. Faller and F. Baumgarte, “Binaural Cue Coding—Part II: Schemesand applications,” IEEE Trans. on Speech and Audio Proc., vol. 11, no.6, November 2003.

1. (canceled)
 2. A method for synthesizing a plurality of audiochannels, comprising: retrieving from an audio stream at least one sumsignal representing a sum of source signals, retrieving from the audiostream statistical information about one or more source signals,receiving from the audio stream, or determining locally, parametersdescribing source mixing parameters, wherein the output audio format isa stereo output audio format, computing output mixer parameters from thereceived statistical information, and the source mixing parameters, andsynthesizing the plurality of audio channels from the at least one sumsignal based on the computed output mixer parameters, wherein thecomputing the output mixer parameters comprises calculating gain factorsand an inter channel coherence (ICC) value for the stereo output audioformat.
 3. The method of claim 2, wherein the statistical informationrepresents spectral envelopes of the source signals, spectral envelopesof the one or more source signals comprise lattice filter parameters orline spectral parameters, or a relative power as a function of frequencyand time of the plurality of source signals.
 4. The method of claim 3,wherein the step of computing the output mixer parameters comprisescomputing cues of the plurality of audio channels and computing theoutput mixer parameters using the computed cues of the plurality ofaudio channels.
 5. The method of claim 2, wherein the audio channels aresynthesized in a subband domain of a filterbank.
 6. The method of claim5, wherein a number and bandwidths of the subband domain are determinedaccording to a spectral and temporal resolution of a human auditorysystem.
 7. The method of claim 5, wherein the number of subbands isbetween 3 and
 40. 8. The method of claim 5, wherein subbands in thesubband domain have different bandwidths, and subbands at lowerfrequencies have smaller bandwidths than subbands at higher frequencies.9. The method of claim 5, wherein a short time Fourier transform basedfilterbank is used and spectral coefficients are combined to form groupsof spectral coefficients such that each group of spectral coefficientsforms a subband.
 10. The method of claim 2, wherein the statisticalinformation also includes auto-correlation functions.
 11. The method ofclaim 3, wherein the spectral envelopes are represented as linearpredictive coding parameters.
 12. The method of claim 4, wherein thecomputed cues are level difference, time difference, or coherence fordifferent frequencies and time instants.
 13. An apparatus arranged tosynthesize a plurality of audio channels, the apparatus comprising:means for retrieving from an audio stream at least one sum signalrepresenting a sum of source signals; means for retrieving from theaudio stream statistical information about one or more source signals;means for receiving from the audio stream, or determining locally,mixing parameters, wherein the output audio format is a stereo outputaudio format; means for computing output mixer parameters from thereceived statistical information, and the source mixing parameters; andmeans for synthesizing the plurality of audio channels from the at leastone sum signal based on the computed output mixer parameters, whereinthe means for computing is configured for calculating, as the outputmixer parameters, gain factors and an inter channel coherence (ICC)value for the stereo output audio format.